For nonlinear discrete-time systems, flatness is usually defined by
replacing the time-derivatives of the well-known continuous-time definition
by forward-shifts. More precisely, the flat output is a function of
the state variables, input variables, and forward-shifts of the input
variables. Conversely, the state- and input variables can be expressed
as functions of the flat output and its forward-shifts. This point
of view has been adopted in [1]}, [2]}
and [3]}. With this definition,
the class of flat systems corresponds exactly to the class of systems
which can be linearized by a discrete-time endogenous dynamic feedback
as it is proposed e.g. in [4]}. Recently,
checkable necessary and sufficient differential-geometric conditions
have been derived in [5]} and [6]}.
Furthermore, in [7]} it has been shown
that in the two-input case even a transformation into a certain normal
form is always possible.
